Solve each equation by factoring.

Given: D is the midpoint of AB; E is the midpoint of AC.

Thepotemich [5.8K]

Answer:

The lines DE and BC have the same slope, therefore the two lines, DE and BC, are parallel

Step-by-step explanation:

To prove that DE is parallel to BC, we have;

The slope, m of the lines DE and BC are found from the following equation;

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Where;

(x₁, y₁) and (x₂, y₂) = (b, c) and (a + b + c) for DE, we have;

$Slope, \, m =\dfrac{c - c}{a + b-b} = 0$

Where we have (x₁, y₁) and (x₂, y₂) = (0, 0) and (2a, 0) for BC, we have;

$Slope, \, m =\dfrac{0 - 0}{2a-0} = 0$

Therefore, because the lines DE and BC have the same slope, the two lines DE and BC are parallel.

5 0

3 years ago

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Need answers ASAP

a_sh-v [17]

We know, Volume of a Sphere = 4/3 πr³
v = 4/3 * 3.14 * 18³
v = 4.186 * 5832
v = 24,416.64 cm³

Volume of a Sphere = 4/3 πr³
v = 4/3 * 3.14 * 12³
v = 4.186 * 1728
v = 7234.56 cm³

Difference = 24,416.64 - 7234.56 = 17182.08

In short, Your Answer would be: 17182.08 cm³

Hope this helps!

6 0

3 years ago

A jar has 15 pink gumballs, 22 green gumballs, 19 red gumballs, and 19 yellow gumballs. Which colored gumball has the greatest p

Phoenix [80]

Answer:

green

Step-by-step explanation:

the one with the most gumballs compared to the other colors is the most likely

7 0

3 years ago

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A warehouse worker moved 108 pallets in 4.5 hours. In minutes, what is the rate to move one pallet? The worker will be off the c

klasskru [66]

Number of pallets moved in 4.5 hours = 108

converting 4.5 hours in minutes we get,

4*60 + 0.5*60 = 240+30 = 270 minutes

So, 108 pallets were moved in = 270 minutes

1 pallet was moved in = $\frac{270}{108}=2.5$ minutes

As the tie will get over in 2 hours or 2*60 = 120 minutes, the number of pallets that can be moved will be = $\frac{120}{2.5}= 48$ pallets.

Hence, 48 pallets can be moved before quitting time.

6 0

3 years ago

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An automobile manufacturer is considering using robots for part of its assembly process. Converting to robots is an expensive pr

LenKa [72]

Answer:

(a) The correct option is: H₀: p = 0.02 vs. Hₐ: p < 0.02.

(b) Explained below.

(c) The better value of α will be 0.10.

Step-by-step explanation:

An automobile manufacturer is considering using robots for part of its assembly process only if there is strong evidence that the proportion of defective installations is less for the robots than for human assemblers.

To test whether the proportion of defective installations is less for the robots than for human assemblers use a single-proportion z-test.

(a)

The hypothesis can be defined as:

H₀: The proportion of defective installations is same for both the robots and human assemblers, i.e. p = 0.02.

Hₐ: The proportion of defective installations is less for the robots than for human assemblers, i.e. p < 0.02.

The alternate hypothesis is the claim or the statement that is being tested.

In this case we need to test whether the proportion of defective installations is less for the robots than for human assemblers or not, so that the manufacturer can decide whether they want to apply the conversion.

Thus, the correct option is:

H₀: p = 0.02 vs. Hₐ: p < 0.02.

(b)

A type I error occurs when we discard a true null hypothesis and a type II error is made when we fail to discard a false null hypothesis.

In this case a type I error will be committed if conclude that the proportion of defective installations is less for the robots than for human assemblers when in fact it is not.

And a type II error will be committed if we fail to conclude that proportion of defective installations is less for the robots than for human assemblers.

(c)

The power of the test is the probability of rejecting a false null hypothesis.

The power of the test sis affected by the significance level of the test (α).

Lesser the significance level of the test the lesser is the power of the test.

If the value of α is reduced from 0.05 to 0.01 then the region of acceptance will increase. This implies that there is low probability of rejecting the null hypothesis even when it is false.

So higher the value of α the higher is the probability of making a correct decision.

Thus, the better value of α will be 0.10.

3 0

3 years ago